Question

The letters of the word $\text{'}ASSASSIN\text{'}$ are written down at random in a row. The probability that no two $S$ occur together is

• A. $\frac{1}{35}$
• B. $\frac{1}{14}$
• C. $\frac{1}{15}$
• D. None of these

Answer 1

The correct option is B

$\frac{1}{14}$

Calculate the probability for the given condition.

In a word, $\text{'}ASSASSIN\text{'}$, apart from the letter $S$, there are $4$ other letters $\left(A,A,I,N\right)$. It may be arranged in $12$ ways $\frac{4!}{2!}$. Hence, it creates $5$ gaps, Of these $5$ gaps, any $4$ gaps can be chosen to place the letter $S$.

It can be done in $\underset{4}{\overset{5}{C}}$ ways.

Hence, the required probability

$$\begin{gathered} =5\times \frac{4!}{2!}\times \frac{2!\times 4!}{8!} \\ =\frac{1}{14} \end{gathered}$$

Hence, option $\left(B\right)$ is correct.